Higher-order derivatives of first-passage percolation with respect to the environment
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918498725265408 |
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| author | Matic, Ivan Radoicic, Rados Stefanica, Dan |
| author_facet | Matic, Ivan Radoicic, Rados Stefanica, Dan |
| contents | We introduce and study derivatives in first-passage percolation with edge weights given by i.i.d. random variables supported on ${a,b}$. We show that the variance of the passage time can be expressed in terms of these derivatives. We further analyze their structure and establish several fundamental properties and bounds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_08935 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher-order derivatives of first-passage percolation with respect to the environment Matic, Ivan Radoicic, Rados Stefanica, Dan Probability We introduce and study derivatives in first-passage percolation with edge weights given by i.i.d. random variables supported on ${a,b}$. We show that the variance of the passage time can be expressed in terms of these derivatives. We further analyze their structure and establish several fundamental properties and bounds. |
| title | Higher-order derivatives of first-passage percolation with respect to the environment |
| topic | Probability |
| url | https://arxiv.org/abs/2504.08935 |